In theory, this serves 8. In my house it serves 5 as a dinner dish (not a side dish)
First, start the polenta.
1.5 cups polenta
6-7 cups liquid (I use about 4c water and then add milk)
2 tsp salt
2 Tbs butter
Bring the water to a boil, then add the salt. Carefully whisk in the polenta. If you are using a mix of water and milk you don't want to boil the milk - so slowly stir it in after the polenta - make sure you incorporate it well.
Reduce the heat and let it barely bubble for about 20-30 minutes. Add more liquid, if needed. You want to cook it until it has a creamy texture and no bite to the grains.
When it is a texture you like, stir in the butter.
This can be used as is (serve in shallow bowl) or put into molds (like a ramkin) to cool and be used later in a more structured way. (I like the rustic-in-a-bowl way.)
As the polenta bubbles on your back burner, make the mushrooms.
1/4 c. olive oil
1 Tbs butter
2 pounds mushrooms (any will do, but try and make it interesting), sliced
1/4 c. diced shallots (or red onion and garlic)
3-4 sprigs thyme (or 1-2 Tbs dried)
1 c. chicken broth
1 c. white wine
1 Tbs finishing butter
Heat the oil and butter in a big, heavy pan. Dump in the mushrooms and saute until almost cooked through (5-7 minutes). Now add the shallots and thyme and cook another 2 minutes or so. Add the liquids.
Simmer on medium-med high until the liquid is reduced by half (about 20 minutes)
Give the pan a good shake, remove the thyme springs, and then swirl in the butter to finish the sauce.
I serve the mushrooms over the soft polenta in a bowl and grate some parm on top. If you are feeling fancy you could make the polenta ahead and cool it and then fry it in olive oil to make crispy polenta cakes to serve it on.